Question

According to Freundlich adsorption isotherm, which of the following is correct?

• A. \( \frac{x}{m} \alpha P^1 \)
• B. \( \frac{x}{m} \alpha P^{1/m} \)
• C. \( \frac{x}{m} \alpha P^0 \)
• D. All are correct for different ranges of pressure

Hint:

The Freundlich adsorption isotherm describes adsorption at various pressures and shows that the relationship between \( \frac{x}{m} \) and \( P \) changes depending on the pressure range.

Answer 1

The Correct Option is D

Step 1: Understand the Freundlich adsorption isotherm.
The Freundlich adsorption isotherm is given by: \[ \frac{x}{m} = a P^{1/n} \] where \( \frac{x}{m} \) is the amount of adsorbate per unit mass of adsorbent, \( P \) is the pressure, and \( a \) and \( n \) are constants.
The exponent \( \frac{1}{n} \) reflects the degree of adsorption.
Step 2: Behavior at different pressure ranges.
At low pressures, the adsorption is approximately proportional to the pressure, \( \frac{x}{m} \propto P^1 \).
As pressure increases, the adsorption follows \( \frac{x}{m} \propto P^{1/n} \), where \( n \) is greater than 1.
At very high pressures, the system may reach saturation, and the adsorption could approach a constant value \( \frac{x}{m} \propto P^0 \).
Step 3: Conclusion.
All these relations are correct for different ranges of pressure, hence option (d) is correct.